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Integration of metamaterial in tapered hollow core fiber for slow-light propagation.

INTRODUCTION

Communication is the ability of interchanging thoughts, ideas by passing or transmitting the information. The medium through which the message is transmitted decides the speed and accuracy of the data that reaches the destination. Optical fiber, being a transmission channel, plays a vital role in fiber optic communication. Initially, short bundle of unclad fibers are used to transmit the image but with the poor quality. In 1954, Abraham van heel covered the bare fiber with a transparent cladding of lower refractive index, which could reduce loss in the transmission. Then the attenuation is greatly reduced to 20 dB/km for a single mode fiber, which would be practical for communication as stated by R.F Keams and Basch in 1998. S. Kawakami and Nishida with their experiments introduced double clad fibers, which could reduce the dispersion in optical fibers. Recent days, metamaterials have attracted many researches as they offer qualitatively new properties, which are initiated by the theory of V.G. Veselago in 196 and developed further by R. A. Shelby, M. Lapine in later years. These are the artificial materials exhibit the properties that are not available in nature, such as backward propagation, negative index of refraction and so on. In this paper, optical fiber is designed with tapered core and a metamaterial cladding, which could be used reduce the group velocity of the fiber to the greater extend when compared to the fiber with no tapering fiber. However, numerous analytic experiments have been made on metamaterial based fibers by many scientists like Kim K Y to prove the transmission of slow light, but they focus less on practical implementation. Use of metamaterials with anisotropy, makes the design of fiber at the optical wavelength easier, while it is difficult with isotropic metamaterials, which was experimented by researchers like Dolling G, et al., and Yao J, et al., over the recent years.

In this paper, tapered core is used instead of cylindrical core so as to make the light travel with the lesser group velocity and also to stop the light at the fixed position efficiently. Previous work by Qi Zhang, et al., related to slow-light propagation has been made of cylindrical fiber with metamaterial cladding and dielectric as core. But the trapping of light is made much easier here, using of hollow tapered core fiber with an anisotropic metamaterial (AMM) cladding. Two different metamaterials of different combinations are used here, so that the suitable metamaterial for effective slow light propagation can be easily identified. The combined silver and [Al.sub.2][O.sub.3] layers act as an AMM, which is evident from the experiments of Elliot J. Smith, et al,. Ag/Si[O.sub.2] layers are other perfect combinations to have perfect metamaterial possessing anisotropic characteristics. This tapered light that stands still at a fixed position is clearly viewed using frequency domain analysis. Energy density variation along the length of the fiber is also plotted to ensure the stopping of light at the specific degeneracy point.

Design Mechanisms:

2.1 Hollow core cylindrical fiber with AMM cladding:

Consider the Electromagnetic (EM) wave propagating inside a hollow core cylindrical waveguide with an AMM cladding and z-axis as the axis of propagation as shown in the Fig. 1(a). Then the Maxwell's equations of an Electromagnetic wave propagating inside a cylindrical waveguide as per the research work of Harrington in the year 2001, is given by the following equations as,

E = [E.sub.0] (r, [phi]) exp [i([beta]z-mt)] (1)

H = [H.sub.0] (r, [phi]) exp [i([beta]z- [omega]t)] (2)

where [omega] and [beta] are the frequency and the wavenumber of the EM wave propagating inside the fiber respectively, and (r, [phi],z) are the cylindrical co-ordinates of the waveguide. For any electromagnetic wave travelling inside a fiber, two important parameters to be considered are their permittivity and permeability. As the AMM is formed by alternating layers of metal/dielectric films, the effective permeability is taken as [mu] = 1 for simplification and the effective permittivity is in tensor form, which is taken in simple diagonal form as

[[epsilon].sub.eff] = diag[[[epsilon].sub.x], [[epsilon].sub.y], [[epsilon].sub.z],] (3)

In 2006, Wangberg R with his co-researchers had defined the values of diagonal elements [[epsilon].sub.x], [[epsilon].sub.y], and [[epsilon].sub.z], which are described by the following equations as,

[[epsilon].sub.x] = [[epsilon].sub.y] = (1 - N) [[epsilon].sub.1] + N [[epsilon].sub.2] (4)

[[epsilon].sub.z] = [[epsilon].sub.1] [[epsilon].sub.2]/ [N [[epsilon].sub.1] + (1-N) [[epsilon].sub.2]] (5)

where [[epsilon].sub.1] and [[epsilon].sub.2] are the permittivity of dielectric and metal layers that are combined to form AMM respectively and N is the volume fraction of the first medium. First, we analyze the propagation of light through a cylindrical waveguide without tapering and with AMM as cladding, which is clearly shown in Fig. 1(b). Here, the alternate layers of metal oxide ([Al.sub.2][O.sub.3]) and a negative permittivity medium (Ag) forms the metamaterial with excellent anisotropy.

The core of the fiber is filled with air and has the diameter of 200 nm, which is maintained till the end of the fiber of distance 10 pm. This makes obvious that there is no tapering in the fiber core. Fig. 1(c) shows the electric field distribution along the z-direction, which is obtained by the Frequency domain study of the designed fiber. It is evident from the Fig. 1(c) that a cylindrical fiber with AMM cladding could guide the electromagnetic wave throughout the entire length of the fiber with no change in velocity or amplitude. The light that enters the fiber reaches the other end with the same electrical energy along the fiber length. Hence in order to reduce the group velocity of the light travelling through the fiber, the core of the fiber is tapered to certain critical diameter. It is also to be noted from the Fig 1(c) that the electromagnetic waves propagate both forward and backward. This possibility of backward and forward propagation is because of the use of metamaterial in the fiber.

2.2 AMM clad fiber with tapered hollow core:

Multilayered structure having alternate layers of metal/dielectrics is used as an AMM could be used as a cladding layer and it is proven fron the experiments of Wood B, et al., in the year 2006. The effective dielectric permittivity tensor of the multilayered stucture can be calculated using the equation (3). Here, two different metamaterials made of different metal and dielecric layers are used, which could support both forward and backward propagation and also helps in anisotropy depending upon the frequency.

[FIGURE 1 OMITTED]

The schematic diagram of linearly tapered waveguide with AMM cladding is shown in the Fig. 2(a). Lateral section of the designed waveguide is shown in the Fig. 2(b), which has the initial core diameter as 200 nm and tapered down to 100 nm over the distance of 10 pm. Fig. 2(c) shows the frequency domain analysis which is simulated with the parameters as [[epsilon].sub.1] = 3.2263, [[epsilon].sub.2] = -1.3416 and N is taken as 75% of volume fraction. Here the parameters [[epsilon].sub.1] and [[epsilon].sub.2] corresponds to the permittivities of [Al.sub.2][O.sub.3] and silver respectively. The effective permittivity is calculated using the equations (3), (4) and (5). The values [[epsilon].sub.x] = [[epsilon].sub.y] is -0.1996 and [[epsilon].sub.z] is found to be 2.0766 at the wavelength of 354 nm.

Unlike the field distribution shown in Fig 1(c), the electric field distribution along the z-direction shown in the Fig. 2(c) shows that the light guided is stopped and stands still before it reaches the end of the waveguide. Fig. 2(d) shows the electric filed distribution for waveguide with same geometry but with the difference in the AMM used in the cladding. Material parameters in this case are [[epsilon].sub.x] = 3.9, [[epsilon].sub.2] = -1.3416 which corresponds to the permittivity of silicon dioxide and silver respectively. At the same incident wavelength of 354 nm, we have [[epsilon].sub.1] = -0.528 and [[epsilon].sub.2] = -3.207. It is to be noted that, if Si[O.sub.2]/Ag layers are used as AMM, the propagation of light is stopped with enhanced amplitude even before the point when [Al.sub.2][O.sub.3]/Ag layers are used. This could be easily identified with the help of the energy density plot that is shown in the Fig. 3(a) and 3(b). The loss effect of the metamaterial at the cladding is compensated by incorporating gain into the core of the fiber, which is shown by the experiments of Jiang T and his colleagues in the year 2009. Tsakmakidis, et al., presented an article theat supports the major reason for tapering the core is that the group velocity of the electromagnetic wave decreases while the radius of the dielectric core reduces to the critical radius at certain excitation frequency. The guided oscillatory wave is then said to stand still, when this group velocity becomes zero.

[FIGURE 2 OMITTED]

2.3 Energy density, Group velocity and Dispersion:

The energy density along the length of the fiber can be plotted to find the degeneracy point at the particular frequency. Light wave is incident with the frequency of 647.5 THz. The point where the light wave stops is found to be at 8 [micro]m of total length, when [Al.sub.2][O.sub.3]/Ag layers are used for cladding, which shown in the Fig. 3(a). For the same incident frequency, the degeneracy point is found to be at 7 [micro]m of the total length as shown in Fig. 3(b), when Si[O.sub.2]/Ag layers are used as AMM in the same geometry of fiber. Therefore, the radius of the core at the length of 8 [micro]m and 7 [micro]m, is the critical radius and the incident frequency of 647.5 THz is the critical frequency for the fiber with [Al.sub.2][O.sub.3]/Ag and Si[O.sub.2]/Ag layers as AMM cladding respectively.

The group velocity ([V.sub.g]) varies with the reduced wavenumber ([k.sub.0]a), which is shown by the graph plotted in Fig. 4. The value of group velocity gradually reduces to zero as the value of [k.sub.0]a decreases, which means that the light wave is slowed and made to stand still at the degeneracy point. It is difficult to make the group velocity to zero in practice, where material losses are taken into consideration, which could be compensated by incorporating gain into the fiber. The plot in the Fig. 4 is made for the tapered hollow core fiber with Si[O.sub.2]/Ag layers as AMM cladding. The effective index of the fiber is given by [n.sub.eff] = [beta]/[k.sub.0] and [k.sub.0] is the wave number in the free space. The graph plotted between the effective index and the reduced wavenumber is shown in the Fig. 5 and it is the dispersion curve of the designed fiber with Si[O.sub.2]/Ag layers as AMM cladding, which indicates that slow-light propagation can take place efficiently through the structured fiber.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Conclusion:

In this paper, slow-light propagation is investigated by frequency domain method for two different AMM cladding in a tapered core fiber. A cylindrical waveguide with no tapering is also designed by using same material parameters and simulated to validate the propagation of light. The use of alternative Si[O.sub.2]/Ag layers and [Al.sub.2][O.sub.3]/Ag layers, which acts as the AMM, supports the propagation of electromagnetic waves both in forward and backward direction in the tapered core fiber. At the critical radius, the group velocity of the propagating light wave becomes zero as these forward and backward merge together. The combination of negative epsilon medium ([A.sub.g]) and the dielectric Si[O.sub.2] layers, proves to be a suitable AMM that supports slow-light propagation efficiently. Variation of group velocity and effective index with the reduced wavenumber are plotted for characterizing the slow-light. Thus the designed fiber is more compatible and can be used to design optical buffers in optical communication networks.

REFERENCES

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(1) R. Yamunadevi, (2) D. Shanmuga sundar, (3) A. Sivanantha Raja

(1) Electronics and Communication Engineering Department, Alagappa chettiar College of Engineering and Technology, Karaikudi--630 0003 INDIA

(2) Electronics and Communication Engineering Department, Alagappa chettiar College of Engineering and Technology, Karaikudi--630 0003 INDIA

(3) Electronics and Communication Engineering Department, Alagappa chettiar College of Engineering and Technology, Karaikudi--630 0003 INDIA

Received 27 May 2016; Accepted 28 June 2016; Available 12 July 2016

Address For Correspondence:

R. Yamunadevi, Electronics and Communication Engineering Department, Alagappa chettiar College of Engineering and Technology, Karaikudi- 630 0003 INDIA

Mob: 91-9943202553; E-mail: yamunrajendran@gmail.com
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Author:Yamunadevi, R.; sundar, D. Shanmuga; Raja, A. Sivanantha
Publication:Advances in Natural and Applied Sciences
Date:Jun 30, 2016
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